J. Phys. Chem. 1993,97, 12205-12209
12205
AM1 Study of the Electronic Structure of Coumarins P. K. McCarthy and G. J. Blancbard' Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 Received: June 21, 1993; In Final Form: August 23, 1993"
W e report our calculations on a series of coumarin molecules. Using semiempirical methods with an AM1 parametrization, we have calculated the ground-state, first excited triplet state, and first excited singlet state energies and dipole moments as well as their dependence on the geometries of different labile side groups. W e find that for all of the coumarins there are excited triplet states in close energetic proximity to the excited singlet states, and the relative ordering of these states depends on the substituents attached to the coumarin chromophore.
Introduction The coumarins are a family of molecules that have been studied extensively because of their application as laser dyes and their substantial state-dependent variation in static dipole moment.' Indeed, this latter property gives rise to characteristically large Stokes shifts, sometimes on the order of 100 nm. These large static Stokesshifts, incombination with their broad and featureless linear responses in solution, have attracted attention to the coumarins as probe molecules for the examination of ultrafast solvation effects.2" Several of these experimental investigations have found that, subsequent to excitation with a short laser pulse, the coumarin fluorescence spectrum evolves in time from an initially blue-shifted feature to the static emission profile, and the time over which this spectral evolution occurs can be correlated with various solvent properties, such as Debye longitudinal relaxation time, TL. The mechanism put forth for the observed spectral evolution is that excitation of the coumarin molecule creates instantaneously a species with a substantially larger dipole moment than was present before the excitation, and the solvent surrounding this newly formed dipolar species must reorganize to accommodate to its presence.2+6 Because this reorganization is not instantaneous, the excited coumarin derivative finds itself initially in a nonequilibrated environment, and its excited electronic state is thus higher in energy than at times long after excitation. The reorganization of the local solvent environment is thought to mediate the relaxation of the coumarin excited state to its steady-state geometry and energy. Several investigators have raised questions regarding the origin of the spectral relaxation properties observed for the coumarins, on the basis of both theoretical considerations9and experimental evidence.* The mechanism postulated for the transient spectral relaxation assumes implicitly that intramolecular processes in the coumarins, such as vibrational relaxation and intersystem crossing, are unimportant, at least on the time scale of the solvent reorganization. Given these assumptions, the measured response arises solely from intermolecular processes and the emission band is treated as a single spectral feature. If the absorption and emission bands of the coumarins can truly be treated as individual features, i.e. if they are homogeneously broadened, then at least vibrational population relaxation within the coumarins can be ignored. The featureless fluorescence band of most coumarin derivativesis on the order of 3OOOcm-1 wide, and their fluorescence lifetimes are typically 5 ns, yielding a time-bandwidth product of AvAt 4.5 X 105. The transform-limited time-bandwidth product expected for a homogeneous line is 0.22,lOand therefore, the emission response of coumarin derivatives exhibits substantial inhomogeneous broadening. Thus, we need to consider the
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Author to whom correspondence should be addressed. *Abstract published in Aduance ACS Abstracts, November 1 , 1993.
possible contribution of intramolecular relaxation processes to the transient spectral shifts measured experimentally. We examined the transient stimulated emission response of coumarin 153 recently and found experimental evidence for multiple electronic states within its emission manifold.* In order to elucidate the identity of these electronic states, we performed a series of semiempirical calculations, and the results indicated the presence of several electronic states within the experimental bandwidth of the coumarin 153 spontaneous emission profile. We present in this paper a series of semiempirical calculations on coumarin and several coumarin derivatives. The purpose of these calculations is to determine the extent to which this family of molecules exhibits multiple excited electronic states in close proximity to one another and how conformational effects for coumarins with labile side groups affect the ordering and energetic separation of these excited states. We find that, for all the coumarin derivatives we have studied, there are several electronic states in close proximity to the SI,and the ordering of these states depends sensitively on the identity and conformation of substituent groups.
Calculations Austin Model 1 (AM 1) semiempirical molecular orbital calculations were performed on the molecules shown in Figure 1 using Hyperchem software. The AM1 semiempirical method''-13 is a modification of MND0,'4Js offering more accurate parametrizations for polar systems and transition states. For our calculations, the geometry of a given molecule was first optimized at the empirical level using an MM+ molecular mechanics routine16 followed by unrestricted geometric optimization at the semiempirical level using an SCF calculation. For several of the coumarins there was found to be more than one stable conformation, and for these species we continued optimization until the lowest energy conformation was found. Electronic energy calculations were performed on the geometrically SCF-optimized molecule for the SO,SI, and TI electronic states. For all electronic energy calculations, the ground-state (SO)optimized geometry was used and the RHF closed-shell calculations were performed using configuration interaction with 100 microstates. The use of this many microstates in the CI calculation provides what we believe to be a fair representation of correlation effects in the coumarins. We found that electronic transition energies were slightly smaller (-5 kcal/mol) for CI calculations than for S C F calculations, as is expected for the inclusion of correlation effects. We chose to use the AM1 parametrization for our calculations because it is known to be optimized for polar systems. For the coumarins shown in Figure 1f, dimethylamino end groups were used in place of diethylamino end groups for computational simplicity. This substitution yielded no changes in electronic-state energies or dipole moments.
0022-365419312097-12205%04.00/0 0 1993 American Chemical Society
McCarthy and Blanchard
12206 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
TABLE I: Calculated Prowrties of Several Coumarins energy relative to So (cm-l) coumarin coumarin 4 coumarin 138 coumarin 6 coumarin 30 coumarin 120 coumarin 151 coumarin 1 coumarin 152 coumarin 102 coumarin 153 coumarin 334 coumarin 337 coumarin 343
-37.31 -90.58 -37.15 +37.28 +57.88 -47.87 -190.68 -35.90 -179.45 -54.63 -197.61 -84.33 -13.18 -133.56
27 189 26 918 25 443 24 486 26 712 26 315 25 083 25 913 25 094 24 731 24 049 25 135 24 804 25 139
30 866 29 999 27 354 25 106 26 872 28 796 26 702 27 865 25 848 26 749 24 675 25 422 25 040 25 206
31 479 31 241 29 269 26 884 28 295 29 896 28 546 29 830 28 190 28 914 27 081 27 505 27 229 27 396
33 754 31 431 29 352 30 381 33 904 30 991 30 187 30 253 30 317 28 659 28 168 27 340 27 183 27 436
4.82 4.14 5.97 7.00 8.06 6.03 6.04 6.35 6.32
5.09 3.66 6.90 9.62 8.96 6.29 8.38 7.78 10.08 8.14 10.86 10.19 12.26 13.47
6.43
6.68 7.39 9.68 10.41
6.21 5.32 8.45 8.60 7.82 8.19 11.27
9.81 13.11
10.09 13.64 12.77
15.11 15.70
(a)
-
c
t J
FH3
,’ ,,’ k
(b)
(0)
24000
25000
26000
27000
28000
29000
30000
calculated So-S, transition energy (cm-’) Figure 2. Comparison of experimental absorption maxima (ref 17) to the calculated 0-0 transition energies for the coumarinsshown in Figure 1: a = coumarin 153; b = coumarin 337; c = coumarin 6; d = coumarin 343;e =coumarin 334; f = coumarin 152;g = coumarin 102;h =coumarin 151; i = coumarin 30; j = coumarin 138; k = coumarin 1; 1 = coumarin 120; m = coumarin 4. Figure 1. Structures of the coumarin molecules for which AM1 calculations were performed. Only one resonance structure is shown for each molecule: (a) coumarin; (b) coumarin 4; (c) coumarin 138; (d) X = S for coumarin 6; X = NCH3 for coumarin 30; (e) R = H for coumarin 120; R = F for coumarin 151; (0R = H for coumarin 1; R = F for coumarin 152; (8) RI= CH3 and Rz = H for coumarin 102; Rl = CF3 and R2 = H for coumarin 153; RI= H and Rz = COCH, for coumarin 334; RI= H and Rz = CN for coumarin 337; RI= H and Rz = COOH for coumarin 343. In addition to calculation of the electronic-state energies of the geometrically optimized coumarin derivatives, we calculated the geometry dependence of the ground-state, first excited singlet state, and first triplet state energies for two labile coumarins. For coumarin 1, the dimethylamino group was rotated about its bond to the coumarin ring system, and for coumarin 6, the benzothiazolyl group was rotated about its bond to the coumarin ring system. The electronic-state energies reported for these calculations were likewise obtained using the AM 1 parametrization with configuration interaction.
Resdts and Discussion Our purpose in performing these calculations was to elucidate the generality of the state ordering and proximity that we observed experimentally for coumarin 153.* Related questions that we investigated were the effect of chemical substitution on the transition energies and state ordering for the coumarins, and the extent to which we expect conformational freedom in labile coumarins toaffect their optical response. We present the results of our semiempirical calculations for the geometrically optimized coumarins in Table 1.
The data in Table I contain several qualitative trends, a t least some of which may be compared to experimental data in the literature. The first trend is that the energy of the So SI transition decreases with increasing substitution to the coumarin chromophore, in qualitative agreement with experimental data.1’ We show in Figure 2 thecorrelation between experimental liquidphase absorption maxima and calculated transition energies. This correlation is not strictly valid because we a r e comparing SO(u-0) Sl(u=O) calculations to So(u=O) Sl(u=n) experimental data, where n is largely unidentified. Despite this mismatch, we do expect a correlation because of the similarity of the SIsurface for all of the coumarins. The modest deviations from a direct correlation reflect subtle substituent-dependent variations in the Franck-Condon factors for the experimental absorption data as well as unaccounted-for solvent polarity effects. In addition to a qualitative correlation, we note that our calculated results for So+ SI transition energies are in good agreement with experimental gas-phase origin measurements for the few coumarins for which the origin has been measured18 (Table 11). On the basis of these correlations with experimental data, we believe that our calculations reflect the electronic properties of the coumarins accurately. Our calculations show that there are several electronic states in close proximity to the SI: the T2, Sz, and T3 states. While this generalization holds for all of the coumarins, we observe that the chemical identity of the substituents of the coumarin chromophore can alter the relative ordering ofthestates. It may betemptingtoviewchangesinstateordering as significant in and of themselves, but it is clear from a careful examination of the data in Table I that these variations arise
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The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12207
AM1 Study of the Electronic Structure of Coumarins
TABLE 11: Comparison of Experimental and Calculated 0-0 Transition EnerPieS. calculated energy exptl0-0 planar amino group twisted amino group (cm-1) (cm-1) (cm-1) molecule 26 702 29 502 coumarin 15 1 28 060 25 848 29 169 coumarin 152 26 687 coumarin 153 25 196 24 675 NIA a The planar amino group heading refers to a calculation where the amino group dihedral angle with respect to the coumarin ring system was optimized at woo. The twisted amino group refers to calculations where a stable conformation of the amino group was at -90° with respect to the coumarin ring system. Experimental data were taken from ref 18. TABLE 111: Calculated Triplet-Triplet Absorption Energies and the Energetic Displacement of the TI State from the SO Ground State transition energy for TI-T. (cm-I) coumarin coumarin 4 coumarin 138 coumarin 6 coumarin 30 coumarin 120 coumarin 15 1 coumarin 1 coumarin 152 coumarin 102 coumarin 153 coumarin 334 coumarin 337 coumarin 343
21 085 20 214 17 630 16 518 17 116 19 166 17 265 18 674 16 909 18 119 16 170 16 909 16 499 16 581
5432 8358 8164 1997 9442 7643 8255 1601 8094 7262 8224 8432 7969 8589
6595 8852 9477 10224 10410 8574 9851 8195 9909 8013 9612 9702 9429 9950
14 168 9895 12 221 11 400 11 295 10 471 11 924 10 560 11 809 9409 11 631 10 932 10 933 11 263
15 434 13 606 14 010 20 137 18 948 12 679 12 920 12 920 12 865 12 223 12 354 12 304 12 274 12 262
from slight changes in energies for states that lie in very close energetic proximity to one another. In addition to calculating the singlet transition energies, we have calculated the triplet-triplet transition energies and indicate certain of these in Table 111. We have listed the energies for transitions between TI and T2 through Ts, and these transitions lie in the energy range -8000 to -13 000 cm-'. Transitions between the TIstate and higher lying triplet states fall in a band between -20 000 and 27 000 cm-I, and these transitions may play a significant role in the transient optical response of coumarins.Is21 Experimental data has shown that triplet-triplet absorption can play an important role in the photophysics and lasing efficiency of these coumarin derivatives, but the spectra show these resonances to be broad and relatively featureless. It is therefore not possible to make a direct comparison between our calculated results and individual T-T resonances observed experimentally. Some polar organic molecules, most notably the oxazines, exhibit significant shifts in electronic charge at their heteroatom sites on excitation, giving rise to state-dependent dynamical properties.22-2' The coumarins, however, do not exhibit this same characteristic. We present inTable IV and Figure 3 our calculated results for SOand SIcoumarin 1. The majority of the statedependent charge shifts occur within the ring structure, and there is little state dependence to the charges on either the heterocyclic oxygen or keto oxygen. We note that, on excitation, the dimethylamino nitrogen of coumarin becomes more positive by -0.1 le, but there appears to be no significant negative charge accumulation a t the keto oxygen. These results for coumarin 1 are representative of those for the other derivatives we report here. It may therefore be misleading to consider the excited states of the coumarins as zwitterionic, as is typically indicated in the literature.' The majority of the change in dipole moment seen on excitation is calculated to occur as a consequence of charge redistribution within the coumarin ring structure and along the N - C axis. The dipole moment change on excitation occurs
TABLE I V Calculated Atomic Charges, Expressed as Decimal Fractions of an Electron Charge, for Coumarin 1. atom no. (Figure 3) SOcharge SI charge A(charge) (SI+) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 21 28
-0,196 +0.045 -0.217 -0.235 +0.138 -0.187 -0.043 -0.251 +0.334 -0,298 -0.073 -0.070 +0.135 +O. 166 +0.087 +0.069 +0.084 +0.075 +O. 153 -0.284 -0.195 +0.097 +0.097 +0.097 +0.093 +O. 160 +0.093 +0.083
-0.180 -0.034 -0.118 -0.152 +0.114 -0.008 -0.183 -0.329 +0.308 -0.326 -0.092 -0.092 +O. 142 +0.161 +0.093 +0.089 +0.093 +0.09 1 +0.008 -0.169 -0.168 +0.087 +0.087 +0.086 +0.133 +0.155 +0.108 +0.096
+0.016 -0,079 +0.099 +0.083 -0.024 +0.179 -0.140 -0.078 -0.026 -0.028 -0.019 -0.022 +0.007 -0.005 +0.006 +0.020 +0.009 +0.016 -0,145 +0.115 +0.027 -0.010 -0.010 -0.01 1 +0.040 -0.005 +0.015 +0.013
The atom numbers corresponding to this table appear in Figure 3.
I
"c H' 15
!4 26
"',H
LH
27
16
Figure 3. Structure and atom number assignment for coumarin 1. Partial charges are given for each atom for the SOand SI statcs in Table IV.
primarily along the 2-6-19-20 molecular axis (Figure 3) and involves very little contribution from either of the oxygens. Some of the utility of these calculations lies in their ability to predict the state-dependent change in dipole moment accurately. We show in Table I our calculated ground-state (SO), excited triplet state (TI), and excited singlet state (SI) dipole moments. The dipole moments for the coumarins have, in general, not been measured, and therefore, a direct comparison of our calculated results to experimental data is not possible. The dipole moment for SOcoumarin has, however, been reported, M = 4.62 D,28 and we calculate the dipole moment for SOcoumarin to be 4.82 D. Maroncelli and Fleming have reported a calculated dipole moment of 4.58 D for coumarin using an MNDO parametrization? but we have chosen to use the AM 1 Hamiltonian because of its better parametrization for polar and excited-state systems. The dominant trends in our calculated results are that the SIdipole moment is typically 50-100% larger than that of the corresponding groundstate species and the TI dipole moment is usually intermediate between those of the SOand the S1. There are some significant exceptions to this trend, especially with the more highly substituted coumarins, and we believe these exceptions to arise from partial cancellation of the coumarin moiety dipole moment by that of
McCarthy and Blanchard
12208 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
s, b
.
b
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b
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I3O[ 120 b
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.*
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30
80
90
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0
30
60
90
120
150
180
dihedral angle ( O )
Figure 4. Calculated energy dependence of the dimethylamino group rotation for the SO,TI, and SIstates of coumarin 1. The dihedral angle is the angle made by the amino group with respect to the coumarin chromophore. Missing points indicate a failure of the calculation to converge at the given dihedral angle.
the labile substituent. Thecoumarins with fluorinated substituents exhibit the largest changes in dipole moment on excitation, presumably because of the strong electron-withdrawing character of the trifluoromethyl group at the 2-position. The addition of substituents at the 8-position (Figure 3) of the coumarin chromophore can have a profound effect on the dipolar properties of the molecule. Coumarins 337 and 343, for example, have comparatively large ground- and excited-state dipole moments because of the presence of the cyano and carboxylic acid groups, respectively. For coumarins 6 and 30, where the 8-substitutent is substantially larger, the state-dependent change in dipole moment becomes much smaller, likely due to partial cancellation of the dipole moments from the two ring structures. Interpretation of the results for coumarins 6 and 30 may be more complicated than that for many of the other coumarins because the benzothiazolyl and benzimidazolyl side groups on coumarins 6 and 30 distort the coumarin ring structure to a slightly nonplanar geometry. We focus now on the effect of conformation on the calculated electronic properties of the coumarins. Indeed, the rotational freedom of substituents to the coumarin ring structure has been invoked as a possible explanation for the complicated and solvent polarity-dependent electronic response of several coumarin derivatives. In the course of our calculations we noted that the transition energies depend on the dihedral angle between the dimethylamino group and the coumarin ring system for molecules where theaminogroup was not " r i g i d i d " andalsoon thedihedral angle made by groups attached to the coumarin ring system at the 8-position. To explore the dependence of the calculated transition energies on the rotational conformation of the substituents, we have used two representative coumarin derivatives, coumarins 1 and 6. We find that the potential energy surfaces for rotation of either group vary with electronic state and also according to which group is rotated. We show in Figure 4 our calculation of the state energy as a
180
c
40t
SO
150
r
3 0 ~ " " ' 1 " " ' 1 " " ' 1 " " ' 1 " ' " 1 " " ' ~ 0 30 60 90 120 150
180
dihedral angle ( O )
Figure 5. Calculated energy dependence of the benzothiazolyl group rotation for the SO,TI,and SIstates of coumarin 6. The dihedral angle is the angle made by the benzothiazolyl group with rsepect to the coumarin chromophore. Missing points indicate a failure of the calculation to converge at the given dihedral angle.
function of dimethylamino group rotation for the SO,T I , and SI states of coumarin 1. There is a significant barrier to rotation of the dimethylamino group in all of the states calculated, but the barrier is higher in the SIand the TIthan the SO.These calculated barrier heights are almost certainly not quantitative; our recent comparison of calculation to experiment for the groundand excited-state barrier heights of DODCI shows that the AM 1 parametrization overestimates the barrier heights, but that the trends predicted by the calculation are c0rrect.2~ Thus, we do not intend this calculation of coumarin 1 to be quantitative, but rather to indicate that the excited singlet and triplet state barriers to amino group rotation in the coumarins are larger than that for the ground state. The observation of a barrier for all of the electronic states calculated indicates the contribution of the amino group orbitals to the A and A* molecular orbitals of the chromophore. The results for rotation of the benzothiazolyl group at the 8-position of coumarin 6 present a sharply different picture, shown in Figure 5 . These calculations indicate an SOand TI rotation barrier of I 1 kcal/mol, indicating that the benzothiazole moiety does not contribute significantly to the ground or first triplet electronmicstatesofcoumarin 6. In the& state, however, there is a substantial barrier to rotation, calculated to be >15 kcal/mol. We interpret this to indicate an increase in doublebond character at the bond joining the benzothiazole and the coumarin subunits. Modification of theaminogroup substituents can affect the energies of both the ground and excited electronic states of coumarin derivatives, whilesubstitution a t the &position will affect only the SI isomerization surface significantly.
Conclusions Our calculations reveal several interesting properties of the coumarins, some of which have been established previously through experimentation. The state dependence of the coumarin dipolemoment varies with theidentityandlocationofsubstituents
AM1 Study of the Electronic Structure of Coumarins
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The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12209
(4) Jarzeba, W.; Walker, G. C.; Johnson, A. E.; Barbara, P. F. Chem. on the coumarin ring system, but with few exceptions, p* Phys. 1991, 152, 57. 1.5--2p. We have also calculated isomerization barriers for two (5) Fee, R. S.;Milsom, J. A.; Maroncelli, M. J . Phys. Chem. 1991, 95, coumarins, one for rotation of a dimethylamino group at the -$171-1 _.-. (6) Maroncelli, M.; Macinnis, J.; Fleming, G. R. Science 1989, 243, 19-position and one for rotation of a benzothiazolyl group at the 1674. 8-position. Rotation of the dimethylamino group affects the (7) Moog, R. S.; Bankert, D. L.; Maroncelli, M. J . Phys. Chem. 1993, ground state and the excited singlet and triplet states of the 97, 1496. (8) Jiang, Y.;Blanchard, G. J. Chem. Phys., in review. molecule. Rotation of the group at the 8-position affects the first (9) Agmon, N. J . Phys. Chem. 1990, 94, 2959. excited singlet state strongly, while having little influence on the (10) Sala, K. L.; Kenney-Wallace, G. A.; Hall, G. E. IEEEJ. Quantum ground or first triplet state. This result offers an opportunity to Elecrron. 1980, 16, 990. predict the optical response of the chromophore as a function of (11) Dewar, M. J. S.;Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. Soc. 1985, 107, 3902. chemical substitution and steric hindrance. The data presented (12) Dewar, M. J. S.;Dieter, K. M. J . Am. Chem. SOC.1986,108,8075. in Table I demonstrate the complexity associated with the optical (13) Stewart, J. J. P. J . Compur.-Aided Mol. Des. 1990, 4, I. response of the coumarins. Because of the multitude of electronic (14) Dewar, M. J. S.;Thiel, W. J. Am. Chem. SOC.1977, 99, 4899. (15) Dewar, M. J. S.;Thiel, W. J . Am. Chem. SOC.1977, 99, 4907. states in closeenergetic proximity to SI, and the known propensity (16) Allinger, N. L. J . Am. Chem. SOC.1977, 99, 8127. of coumarins to intersystem cross to their triplet m a n i f ~ l d , ' ~ - ~ ~ (17) Optical Products. Publication JJ-169; Eastman Kodak Co.; pp 14it appears that the coumarins as a class are less than ideal for 36. (18) Ernsting, N. P.; Asimov, M.; Schafer, F. P. Chem. Phys. Lett. 1982, probing transient photophysical and dynamical processes.
Acknowledgment. We are grateful to the National Science Foundation for support of this research through Grant CHE 9211237, and to the Autodesk Corporation for their donation of the software. References and Notes (1) Drexhage, K. H. In Topics in Applied Physics, Vol. 1, Dye Lasers; Schifer, F. P., Ed.; Springer: Berlin, 1973. (2) Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1987, 86, 6221. (3) Barbara, P. F.; Jarzeba, W. Adu. Phorochem. 1990, 15, 1.
91, 231. (19) Dempster, D. N.; Morrow, T.; Quinn, M. F. J . Phorochem. 1973,2, 329. (20) Pavlopoulos, T. G.; Golich, D. J. J . Appl. Phys. 1988, 64, 521. (21) Priyadarsini, K.I.; Naik, D. B.; Moorthy, P. N. Chem. Phys. Lett. 1988, 148, 572. (22) Blanchard, G. J. Chem. Phys. 1989, 138, 365. (23) Blanchard, G. J. J . Phys. Chem. 1991, 95, 5293. (24) Blanchard, G. J. Anal. Chem. 1989, 61, 2394. (25) Blanchard, G. J. J. Phys. Chem. 1989, 93,4315. (26) Blanchard, G. J. J . Phys. Chem. 1988, 92,6303. (27) Blanchard, G. J.; Cihal, C. A. J. Phys. Chem. 1988, 92, 5950. (28) Griffiths, V. S.;Westmore, J. B. J . Chem. SOC.1963, 4941. (29) Awad, M. M.; McCarthy, P. K.; Blanchard, G. J. J . Phys. Chem., in review.
